Ultrafine BaTiO3 and BaSnO3 powders were prepared by thermal decomposition of oxalates through synthesis by the method of co-precipitation; Dy2O3, Nb2O5 and ZnO, used as dopants, were added to the main constituents, known as the tailor-made Ba(Ti, Sn)O3, according to the indicated compositions, then the batches were mixed until they became homogeneous. Careful treatment was necessary in later stages of the process of ceramic making. The dielectric properties of the ceramics were measured. It was found that high epsilon, low tan delta and low depsilon/dt were characteristics of these ceramics. The results could be explained by the effects of peak shifting, broadening and grain-size inhibition. The relationship between composition, structure and properties is discussed.